On the perturbed Friedmann equations in Newtonian Gauge

TL;DR

This paper offers a heuristic derivation of Friedmann equations using Newtonian mechanics and thermodynamics, demonstrating their consistency with relativistic results and providing educational insights into cosmological dynamics.

Contribution

It introduces a Newtonian and thermodynamic approach to derive Friedmann equations, bridging Newtonian mechanics and General Relativity in cosmology.

Findings

Derivation of Friedmann equations from Newtonian mechanics

Demonstration of consistency with relativistic conservation laws

Pedagogical framework for understanding cosmological dynamics

Abstract

Based on the Newtonian mechanics, in this article, we present a heuristic derivation of the Friedmann equations, providing an intuitive foundation for these fundamental relations in cosmology. Additionally, using the first law of thermodynamics and Euler's equation, we derive a set of equations that, at linear order, coincide with those obtained from the conservation of the stress-energy tensor in General Relativity. This approach not only highlights the consistency between Newtonian and relativistic frameworks in certain limits but also serves as a pedagogical bridge, offering insights into the physical principles underlying the dynamics of the universe.